The thought experiment he invented to demonstrate this idea is defective, as discussed below. A more careful analysis shows that gravity is a general force that can produce a radically different effect than a specific force producing acceleration, say by an engine, a rocket, or an explosion.
Beginning in Chapter 20 of his 1917 Book on Relativity Theory Einstein uses a common sense thought experiment to demonstrate the equivalence of the force of gravity and other, more common known forces, which produce acceleration. His analysis involves a man standing in a box, in the absence of gravitational force, but with a hook and rope attached to the top of the box and an imaginary engine accelerating the box upwards. The man's kinesthetic experience is the same as though the box were standing on earth and gravity were anchoring his feet to the ground. This compelling image is the source of his belief that gravity has the same effect as acceleration produced by any other means.
The facts in the experiment are correct - the conclusion is wrong. To bring this point home an alternative thought experiment is offered which stresses the distinction between the force of gravity and other forces with which we are familiar, such as the force of an engine pulling and accelerating a train, or the powder in a gun which accelerates a bullet to produce its muzzle velocity.
To distinguish the force of gravity from such other forces consider an idealized experiment in which a train is moving along an embankment on a planet on which the force of gravity is negligible. In one case we let an engine accelerate the train. In a second case we imagine a large body ahead of the train which attracts the train due to its gravitational pull. We can also imagine this second case as a train falling, or racing, to earth.
If the train were in uniform motion then it would be valid to compare a walk forward on the train with a laser firing a pulse of light, or a gun shooting a bullet from the rear of the train in the direction of the train's motion. The velocity of the walker, the bullet or the photon remains constant relative to the velocity of the train. But if the train is accelerating because of the engine pulling it this is no longer true. In that case the walker, at each step, is in touch with the instantaneous velocity of the train, so that his walk can remain essentially constant with respect to the instantaneous velocity of the accelerating train. But the bullet or the laser beam do not remain in contact with the train so their velocity will decrease relative to that of the accelerating train as time passes.
On the other hand, if the train were falling towards earth, or pulled forward by a large gravitational mass, the acceleration would be due to gravity and the bullet fired from the gun (and possibly the laser light) would also be subject to the continuing force of gravity so the velocity relative to that of the train would be constant as is the case for the walker. This differentiates the case of gravitational acceleration from the force producing acceleration that acts only on the train.
What is clear is that we have a distinction between a specific force operating on a specific body and a general force, the force of gravity, operating in an undifferentiated way on all bodies, objects, possibly even photons. Since the effects are different in the two cases we cannot claim that the force of gravity is the same as any other force that produces acceleration. The validity of General Relativity, like that of Special Relativity, can therefore be questioned.